# The Two-Halo Term in Stacked Thermal Sunyaev-Zel'dovich Measurements: Implications for Self-Similarity

## TL;DR

This paper investigates the impact of correlated halos on stacked tSZ measurements, revealing potential deviations from self-similar models in the pressure-mass relation of galaxy groups and clusters.

## Contribution

It models the two-halo term in tSZ measurements, highlighting its significance and providing a framework to interpret future high-resolution data for understanding hot gas in low-mass halos.

## Key findings

- Moderate evidence of deviation from self-similarity in pressure-mass relation.
- The two-halo term can bias interpretations if neglected.
- Upcoming experiments will resolve one-halo contributions, refining models.

## Abstract

The relation between the mass and integrated electron pressure of galaxy group and cluster halos can be probed by stacking maps of the thermal Sunyaev-Zel'dovich (tSZ) effect. Perhaps surprisingly, recent observational results have indicated that the scaling relation between integrated pressure and mass follows the prediction of simple, self-similar models down to halo masses as low as $10^{12.5} \, M_{\odot}$. Hydrodynamical simulations that incorporate energetic feedback processes suggest that gas should be depleted from such low-mass halos, thus decreasing their tSZ signal relative to self-similar predictions. Here, we build on the modeling of Vikram, Lidz, and Jain (2017) to evaluate the bias in the interpretation of stacked tSZ measurements due to the signal from correlated halos (the "two-halo" term), which has generally been neglected in the literature. We fit theoretical models to a measurement of the tSZ -- galaxy group cross-correlation function, accounting explicitly for the one- and two- halo contributions. We find moderate evidence of a deviation from self-similarity in the pressure -- mass relation, even after marginalizing over conservative miscentering effects. We explore pressure -- mass models with a break at $10^{14} \, M_{\odot}$, as well as other variants. We discuss and test for sources of uncertainty in our analysis, in particular a possible bias in the halo mass estimates and the coarse resolution of the Planck beam. We compare our findings with earlier analyses by exploring the extent to which halo isolation criteria can reduce the two-halo contribution. Finally, we show that ongoing third-generation CMB experiments will explicitly resolve the one-halo term in low-mass groups; our methodology can be applied to these upcoming data sets to obtain a clear answer to the question of self-similarity and an improved understanding of hot gas in low-mass halos.